Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component... Show moreAnalytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its components singularly perturbed, this component is known as the fast variable. We develop an analytical theory describing the periodic patterns emerging from a Turing instability using geometric singular perturbation theory. We show analytically that after the initial Turing instability, spatially periodic patterns evolve into a small amplitude spike in the fast variable whose amplitude grows as one moves away from onset. This is followed by a secondary transition where the spike in the fast variable widens, its periodic pattern develops two sharp transitions between two flat states and the amplitudes of the other variables grow. The final type of transition we uncover analytically is where the flat states of the fast variable develop structure in the periodic pattern. The analysis is illustrated and motivated by a numerical investigation. We conclude with a preliminary numerical investigation where we uncover more complicated periodic patterns and snaking-like behaviour that are driven by the three transitions analysed in this paper. This paper provides a crucial step towards understanding how periodic patterns transition from a Turing instability to large amplitude. Show less
Easwaran, R.; Khan, M.; Sancheti, P.; Shyam, A.; Bhandari, M.; Ranawat, A.S.; ... ; Rajgopal, A. 2022
Purpose There is a lack of consensus regarding need for Venous Thrombo Embolism (VTE) prophylaxis following arthroscopic knee surgery and open soft tissue knee reconstruction. Clear cut guidelines... Show morePurpose There is a lack of consensus regarding need for Venous Thrombo Embolism (VTE) prophylaxis following arthroscopic knee surgery and open soft tissue knee reconstruction. Clear cut guidelines like ones for trauma surgery and arthroplasty do not exist and the published literature is limited to case reports with a few society guidelines. Given this lack of consensus, we conducted a modified Delphi questionnaire of international experts to provide recommendations on this topic. Methods The consensus statements were generated using an anonymised 3 round modified Delphi questionnaire, sent to an international panel of 38 knee surgeons, with an 80% agreement being set as the limit for consensus. The responses were analysed using descriptive statistics with measures like mode, median and box plots. Feedback was provided to all panelists based on responses from the previous rounds to help generate the consensus. Results Six consensus statements were generated after the three rounds of Delphi. Patient factors, prolonged surgery duration and family history of thrombogenic events emerged as the main points to be taken into consideration for prophylaxis. Conclusion It was established through this study, that there exists a select group of patients undergoing arthroscopic surgery that justify the usage of VTE prophylaxis. The expert responses to most of the questions in different scenarios favoured usage of VTE prophylaxis based on patient factors like advanced age, past history of VTE, smoking, oral contraceptive use etc. Show less
